NEW YORK (CNN/Money) - With the S&P 500 nearing 1,050, the stock market is once again at one of those levels bulls and bears fight over so intensely. It could make for some interesting action.

Yep, 1,050 seems awfully arbitrary, little more than a fat round number that's easy to remember. But people have been keying off it for over a month -- before the S&P broke past its summer high, even, which of course was the last all-important level that everyone was watching.

Justin Lahart, senior writer at CNN/Money, talks about how the S&P 500 index is getting close to 1,050, a level Wall Street is watching closely.

Doug Cliggott, the bearish former J.P. Morgan strategist who is now the bearish head of U.S. research for the hedge fund Brummer & Partners, has identified it as a likely high-water mark for the year. The place that the market should turn tail and run. If it doesn't, he thinks it will be a sign that many big investors who got the market wrong this year have completely caved, and are engaged in a desperate game of catch-up.

Kirlin Securities chief strategist Brian Reynolds is also keying off 1,050, pointing out that this was where the market began its collapse in June of last year. The last day the S&P touched 1,050, in fact, was June 5, 2002 -- the day that former Tyco CEO Dennis Kozlowski was indicted for tax evasion.

It was the point where it really became clear to investors that the deceit in U.S. boardrooms was really much more widespread than they'd thought, and it is the point where the corporate bond market became unhinged, putting companies' ability to get needed financing in doubt. A push through 1,050, then, would suggest the sins of the past have gotten washed away.

Reynolds says the bulls would love to push the S&P through a close above 1,050, but for the moment he doesn't think they're going to get their wish. The recent weakness in Treasurys has made yields too attractive for asset allocators to pass up. With the bond market open again after Monday's holiday, money may flow out of stocks into Treasurys. Once bonds find some stability, however, Reynolds thinks stocks can make another run for it.

If 1,050 does offer the sort of resistance some people think it will, it could become important for the market -- even though all it really is a fat round number. Traders tend to coalesce around such levels, placing bets on whether stocks will bust through or fail, and these tend to make the levels sticky. When the market gets pushed past resistance, however, a lot of people are caught offsides and this adds momentum to the rally.

If this happens here, it may be onward and upward with the market to Dow 10,000, which is the fattest round number of them all -- and the biggest dogfight.